For the International Large Detector (ILD) at the planned International Linear Collider (ILC) a Time Projection Chamber (TPC) is foreseen as the main tracking detector. The TPC will have a single-point resolution of 100~um in Rphi and 0.4-1.4~mm along the Z~axis. The endcap will contain about 240~readout modules. Micro Pattern Gaseous Detectors (MPGD) will be used for gas amplification. The Large Prototype TPC was designed for testing existing and new technologies in conditions as close as possible to those in the ILD TPC. The first part of the studies presented here is devoted to detailed simulations of the response function of the pad-based readout and a triple Gas Electron Multiplier (GEM) stack as a gas system. If the number of activated pads is less than three, the point resolution degrades. This effect may be corrected by applying corrections derived from a fit with the expected Pad Response Function. The second part focuses on the two-hit resolution as a function of the distance between two tracks. It is studied for different track-finding and hit-splitting algorithms for both simulated and experimental data. The main focus of the last part is on studies of the discharge stability and operational features of large-area (22x18cm^2) GEM foils. The effect of voltage oscillations after discharge is studied. The comparison of voltage profiles and Fourier transformations of experimental and simulation data allows the discharge resistance to be estimated (0.6~Ohm). The voltage oscillations have been recognized as a trigger for subsequent discharges (with nanosecond-scale time differences). The growth of a resistive oxide layer on top of a GEM surface has been introduced and studied as a method of GEM protection.